The internal length, breadth and height of a rectangular Box A are 20 cm, 18 cm and 15 cm respectively and that of Box B are 18 cm, 12 cm and 5 cm respectively. The volume of Box A is how many times that of Box B?

Options

A. 4
B. 5
C. 6
D. 3

Answer

To find out how many times the volume of Box A is compared to Box B, we need to calculate the volumes of both boxes first.

### Step 1: Calculate the Volume of Box A
The formula for the volume \( V \) of a rectangular box is given by:
\[ V = \text{Length} \times \text{Breadth} \times \text{Height} \]

For Box A:
- Length \( L_A = 20 \, \text{cm} \)
- Breadth \( B_A = 18 \, \text{cm} \)
- Height \( H_A = 15 \, \text{cm} \)

Now, substituting the values into the volume formula:
\[ V_A = L_A \times B_A \times H_A = 20 \times 18 \times 15 \]

Calculating:
\[ V_A = 20 \times 18 = 360 \]
\[ V_A = 360 \times 15 = 5400 \, \text{cm}^3 \]

### Step 2: Calculate the Volume of Box B
For Box B:
- Length \( L_B = 18 \, \text{cm} \)
- Breadth \( B_B = 12 \, \text{cm} \)
- Height \( H_B = 5 \, \text{cm} \)

Now, substituting the values into the volume formula:
\[ V_B = L_B \times B_B \times H_B = 18 \times 12 \times 5 \]

Calculating:
\[ V_B = 18 \times 12 = 216 \]
\[ V_B = 216 \times 5 = 1080 \, \text{cm}^3 \]

### Step 3: Find How Many Times Volume of Box A is Compared to Box B
To find how many times the volume of Box A is compared to Box B, we divide the volume of Box A by the volume of Box B:
\[ \text{Times} = \frac{V_A}{V_B} = \frac{5400}{1080} \]

Calculating:
\[ \text{Times} = 5 \]

### Final Answer
The volume of Box A is **5 times** that of Box B.

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